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Equivalent Bending Moment of Circular Shaft Formula

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The Equivalent Bending Moment is a bending moment which, acting alone, would produce in a circular shaft a normal stress. Check FAQs

M e = \frac{σ b}{\frac{32}{π \cdot (Φ^{3})}}

M_e - Equivalent Bending Moment?σ_b - Bending Stress?Φ - Diameter of Circular Shaft?π - Archimedes' constant?

Equivalent Bending Moment of Circular Shaft Example

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Here is how the Equivalent Bending Moment of Circular Shaft equation looks like with Values.

Here is how the Equivalent Bending Moment of Circular Shaft equation looks like with Units.

Here is how the Equivalent Bending Moment of Circular Shaft equation looks like.

29.8206 = \frac{0.72}{\frac{32}{3.1416 \cdot (750^{3})}}

29.8206kN*m = \frac{0.72MPa}{\frac{32}{3.1416 \cdot ({750mm}^{3})}}

29.8206 = \frac{0.72}{\frac{32}{3.1416 \cdot (750^{3})}}

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Equivalent Bending Moment of Circular Shaft Solution

Follow our step by step solution on how to calculate Equivalent Bending Moment of Circular Shaft?

FIRST Step Consider the formula

M e = \frac{σ b}{\frac{32}{π \cdot (Φ^{3})}}

Next Step Substitute values of Variables

∴

M e = \frac{0.72MPa}{\frac{32}{π \cdot ({750mm}^{3})}}

Next Step Substitute values of Constants

∴

M e = \frac{0.72MPa}{\frac{32}{3.1416 \cdot ({750mm}^{3})}}

Next Step Convert Units

∴

M e = \frac{720000Pa}{\frac{32}{3.1416 \cdot ({0.75m}^{3})}}

Next Step Prepare to Evaluate

∴

M e = \frac{720000}{\frac{32}{3.1416 \cdot ({0.75}^{3})}}

Next Step Evaluate

∴

M e = 29820.5865164969N*m

Next Step Convert to Output's Unit

∴

M e = 29.8205865164969kN*m

LAST Step Rounding Answer

∴

M e = 29.8206kN*m

Equivalent Bending Moment of Circular Shaft Formula Elements

Variables

Constants

Equivalent Bending Moment

The Equivalent Bending Moment is a bending moment which, acting alone, would produce in a circular shaft a normal stress.

Symbol: M_e

Measurement: Moment of ForceUnit: kN*m

Note: Value should be greater than 0.

Formulas to find Equivalent Bending Moment

Bending Stress

The Bending Stress is the normal stress that is induced at a point in a body subjected to loads that cause it to bend.

Symbol: σ_b

Measurement: StressUnit: MPa

Note: Value should be greater than 0.

Formulas to find Bending Stress

Diameter of Circular Shaft

Diameter of circular shaft is denoted by d.

Symbol: Φ

Measurement: LengthUnit: mm

Note: Value should be greater than 0.

Formulas to find Diameter of Circular Shaft

Archimedes' constant

Archimedes' constant is a mathematical constant that represents the ratio of the circumference of a circle to its diameter.

Symbol: π

Value: 3.14159265358979323846264338327950288

Other formulas in Equivalent Bending Moment and Torque category

Go Maximum Shear Stress due to Equivalent Torque

τ max = \frac{16 \cdot T e}{π \cdot (Φ^{3})}

Go Bending Stress of Circular Shaft given Equivalent Bending Moment

σ b = \frac{32 \cdot M e}{π \cdot (Φ^{3})}

Go Diameter of Circular Shaft given Equivalent Bending Stress

Φ = {(\frac{32 \cdot M e}{π \cdot (σ b)})}^{\frac{1}{3}}

Go Diameter of Circular Shaft for Equivalent Torque and Maximum Shear Stress

Φ = {(\frac{16 \cdot T e}{π \cdot (τ max)})}^{\frac{1}{3}}

How to Evaluate Equivalent Bending Moment of Circular Shaft?

Equivalent Bending Moment of Circular Shaft evaluator uses Equivalent Bending Moment = Bending Stress/(32/(pi*(Diameter of Circular Shaft^3))) to evaluate the Equivalent Bending Moment, The Equivalent Bending Moment of Circular Shaft formula is defined as the reaction induced in a structural element when an external force or moment is applied to the element, causing the element to bend. Equivalent Bending Moment is denoted by M_e symbol.

How to evaluate Equivalent Bending Moment of Circular Shaft using this online evaluator? To use this online evaluator for Equivalent Bending Moment of Circular Shaft, enter Bending Stress (σ_b) & Diameter of Circular Shaft (Φ) and hit the calculate button.

FAQs on Equivalent Bending Moment of Circular Shaft

What is the formula to find Equivalent Bending Moment of Circular Shaft?

The formula of Equivalent Bending Moment of Circular Shaft is expressed as Equivalent Bending Moment = Bending Stress/(32/(pi*(Diameter of Circular Shaft^3))). Here is an example- 0.029821 = 720000/(32/(pi*(0.75^3))).

How to calculate Equivalent Bending Moment of Circular Shaft?

With Bending Stress (σ_b) & Diameter of Circular Shaft (Φ) we can find Equivalent Bending Moment of Circular Shaft using the formula - Equivalent Bending Moment = Bending Stress/(32/(pi*(Diameter of Circular Shaft^3))). This formula also uses Archimedes' constant .

Can the Equivalent Bending Moment of Circular Shaft be negative?

No, the Equivalent Bending Moment of Circular Shaft, measured in Moment of Force cannot be negative.

Which unit is used to measure Equivalent Bending Moment of Circular Shaft?

Equivalent Bending Moment of Circular Shaft is usually measured using the Kilonewton Meter[kN*m] for Moment of Force. Newton Meter[kN*m], Millinewton Meter[kN*m], Micronewton Meter[kN*m] are the few other units in which Equivalent Bending Moment of Circular Shaft can be measured.

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Equivalent Bending Moment of Circular Shaft Formula

Equivalent Bending Moment of Circular Shaft Example

Equivalent Bending Moment of Circular Shaft Solution

Equivalent Bending Moment of Circular Shaft Formula Elements

Other formulas in Equivalent Bending Moment and Torque category

How to Evaluate Equivalent Bending Moment of Circular Shaft?

FAQs on Equivalent Bending Moment of Circular Shaft

Variable Name